3 edition of Morse theory, minimax theory and their applications to nonlinear differential equations found in the catalog.
Morse theory, minimax theory and their applications to nonlinear differential equations
Includes bibliographical references.
|Statement||editors: Haim Brezis ... [et al.].|
|Series||New studies in advanced mathematics -- v. 1|
|LC Classifications||QA372 .M67 2003|
|The Physical Object|
|Pagination||iv, 282 p. ;|
|Number of Pages||282|
introduction to minimax methods in critical point theory and their application to problems in differential equations. The presentation of the abstract minimax theory is essentially self-contained. Most of the applications are to semilinear elliptic partial differential equations and a basic knowledge of linear elliptic the-File Size: 2MB. This session consists of an imaginary dialog written by Prof. Haynes Miller and performed in his class in spring It takes the form of a debate between Linn E. R. representing linear first order ODE's and Chao S. doing the same for first order nonlinear ODE's.
The theorem is valid for higher order equations: the general solution of the non-homogeneous equation is y= y h + y p, where y h is the general solution of the homogeneous equation and y p is any particular solution of the non-homogeneous equation. An Example For equation y00 = 10, the homogeneous equation y00 = 0 has general solution y h = c File Size: KB. analytic Applied Science approximate assume Banach space bifurcation boundary conditions boundary value problem bounded consider construct continuous converges defined denotes derivatives discrete domain element estimate exists finite free boundary global solution Hence holds hyperbolic implicit function theorem implies inequality initial value.
Nonlinear algebraic equations, which are also called polynomial equations, are defined by equating polynomials (of degree greater than one) to zero. For example, + −. For a single polynomial equation, root-finding algorithms can be used to find solutions to the equation (i.e., sets of values for the variables that satisfy the equation). However, systems of algebraic . Chang treats Morse theory as a tool to study multiple solutions to different equations arising in the calculus of variations. Among the topics he covers are basic Morse theory and its various extensions; minimax principles in Morse theory; and applications of semilinear boundary value problems, periodic solutions of Hamiltonian systems, and Price: $
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: Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations (New Studies in Advanced Mathematics) (Vol 1) (): Paul H.
Rabinowitz, Jia Quan Liu, Shu Jie Li, Haim Brezis: BooksAuthor: Paul H. Rabinowitz. Get this from a library. Morse theory, minimax theory and their applications to nonlinear differential equations: held at Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, April 1st to September 30th, [H Brézis;].
The book is based on my lecture notes "Infinite dimensional Minimax theory and their applications to nonlinear differential equations book theory and its applications",Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials Cited by: Purchase Nonlinear Partial Differential Equations and Their Applications, Volume 31 - 1st Edition.
Print Book & E-Book. ISBNHopefully, this topological method would deal with the existence and the multiplicity of solutions of certain nonlinear differential equations. However, in this theory, the manifold is compact, and the functions are assumed to be C 2 and to have only nondegenerate critical points; all of these restrict the applications seriously.
In contrast Cited by: The aim of this book is twofold: (1) to give an introduction to the index theory for symplectic matrix paths and its iteration theory, which form a basis for the Morse theoretical study on Hamilto.
The purpose of this paper is to survey developments in the field of critical point theory and its applications to differential equations that have occurred during the past 20–25 years. This is too broad a theme for a single survey and we will focus on three particular by: Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given.
The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. Nontrivial critical points for asymptotically quadratic functional at resonance, in: Morse Theory, Minimax Theory and their Applications to Nonlinear Differential Equations, in: New Stud Jan The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations.
An expanded version of the author's CBMS lectures, this volume is.  Chang, K.-C. Infinite-dimensional Morse Theory and Multiple Solution Problems, volume 6 of Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Boston Inc., Boston, MA, Cited by: 6.
REFERENCES 1. AMANN H. & ZEHNDER E., Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm.
Sup. Piss 7, (). BENCI V., A new approach to Morse -Conley theory and some applications, Ann. Math. Pura Appl.(). by: The book is based on my lecture notes "Infinite dimensional Morse theory and its applications",Morse Indices of Minimax Critical Points Link # Progress in nonlinear differential equations and their applications.
Brezis, ShuJie Li, JiaQuan Liu and P. Rabinowitz eds. Morse theory, Minimax theory and their Applications in Nonlinear Differential Equations, Proc. Workshop held at the Chinese Acad. of Sciences, Beijing,International Press, 5. Nonlinear Differential Equations: Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations.
This book discusses the exchange of mathematical ideas in stability and bifurcation theory. Organized into 26 chapters, this book begins with an overview of the initial value problem Book Edition: 1.
Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Third Edition 3], [Ergebnisse der Mathematik und ihrer Grenzgebiete, ISSN A series of modern surveys in mathematics Volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete: a series of modern surveys in mathematics.
Folge 3 5/5(1). Devoted to minimax theorems and their applications to partial differential equ Infinite dimensional Morse theory and multiple solution problems (Progress in Nonlinear Differential Equations and T.
Brighi, Bernhard 编 / Birkhauser / / USD refer to the monograph by Rybakowski , and, for a Morse theory based on the Conley index, to Benci . A useful survey of Morse theory in the context of nonsmooth critical point theory is due to Degiovanni .
Morse theory on inﬁnite-dimensional manifolds for functions with inﬁnite Morse index is due to Witten and Floer. There has been a great deal of excitement in the last ten years over the emer gence of new mathematical techniques for the analysis and control of nonlinear systems: Witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos, and other complicated dynamical behavior and the develop ment of a comprehensive theory of Author: Shankar Sastry.
Fundamental Theory ODEs and Dynamical Systems Ordinary Differential Equations An ordinary differential equation (or ODE) is an equation involving derivatives of an unknown quantity with respect to a single variable.
More precisely, suppose j;n2 N, Eis a Euclidean space, and FW dom.F/ R nC 1copies ‚ „ ƒ E E. Rj: ().
Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations, New Stud. Adv. Math., vol. 1, Int. Press, Somerville, MA (), pp. Chapter & Page: 43–4 Nonlinear Autonomous Systems of Differential Equations You may have encountered this creature (or its determinant) in other courses involving “two functions of two variables” or “multidimensional change of variables”.
It will, in a few pages, provide a link between nonlinear and linear Size: KB.The author not only employs Morse theory as a tool to study multiple solutions to differential equations arising in the calculus of variations, but covers a broad range of applications to semilinear elliptic PDE, to dynamical systems and symplectic geometry, and to geometry of harmonic maps and minimal surfaces.